## Abstract In this paper we deduce a necessary and sufficient condition for a line grah to have crossing number 1. In addition, we prove that the line graph of any nonplanar graph has crossing number greater than 2.
On graphs whose line graphs have crossing number one
✍ Scribed by Stanislav Jendrol'; Marián Kles̆c̆
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 118 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0364-9024
- DOI
- 10.1002/jgt.1012
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
Necessary and sufficient conditions are given for a nonplanar graph to have a line graph with crossing number one. This corrects some errors in Kulli et al. 4. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 181–188, 2001
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